I'd like to create a landing page template that doesn't have the header & footer. I know I can use css on the page-id to display:none, but it would be exceedingly awesome to be able to do this with a template. Is it possible? If so, what's the process?

You can create as many templates as you desire. If each is local, don't set it globally, but if you want one to be global, you can make a new template on a page and as you save the template and it's applied there, locally. It should not become global unless you set it to be so.